Mathematics Problem Of the Week

Fall 2006

POW #8

Simple Fractions

We know that any rational number can be written as a fraction a/b where a and b are integers. We’ll define a simple fraction to be a rational number where the numerator is 1.

Obviously we can write any rational number as a sum of simple fractions. For example

But can we always do this where all the simple fractions in the sum are different?

(a) Find a way to express 5/7 as a sum of distinct simple fractions.

(b) Either prove that any positive rational number less than one can be written as a sum of distinct simple fractions or give an example where it is impossible.

Due Friday, November 10^th at Noon.

Solutions should be submitted to Dr. R. Lock's mailbox in the Math office or sent via e-mail to rlock@stlawu.edu.